Research

On this page, you will find a short description of my research interestes, conference attendances as well as my full list of piblications. For a list of past scientific activites, please see my CV.

Research Interests

My primary research interests is in infinite groups, their actions on spaces and their interplay with dynamical systems.

Currently, I have been particularly interested in generalisations of the Higman-Thompson groups and their connections to shift dynamical systems.

I am also interested in connections between group theory and theoretical computer science. In particular, decision problems in groups, cellular automata and groups generated by automata.

“He took his vorpal sword in hand:
Long time the manxome foe he sought–
So rested he by the Tumtum tree,
And stood awhile in thought.”

– Lewis Carroll

Funding information

From February 2024 to January 2027 my research is funded by the Engineering and Physical Sciences Research Council Open postdoctoral fellowship “The Higman-Thompson groups, their generalisations, and automorphisms of shift spaces.”

Publications

Submitted

  1. Conjugacy for certain automorphisms of the one-sided shift via transducers.
    C. Bleak, F. Olukoya.
    Preprint arXiv:2301.13570, 1-53.
  2. Automorphisms of shift spaces and the Higman–Thompson groups: the two-sided case.
    C. Bleak, P. Cameron, F. Olukoya.
    Preprint arXiv:2006.01466, 1-46.
  3. Automorphisms of shift spaces and the Higman–Thompson groups: extensions.
    F. Olukoya.
    Preprint arXiv:2407.18720, 1-50.
  4. An automata theoretic proof that \(Out(T_2)\) is isomorphic to \(\mathbb{Z}/ 2\mathbb{Z}\) and some embedding results for \(Out(V)\).
    F. Olukoya.
    Preprint: arXiv:2003.14372, 1-21.
  5. The core growth of strongly synchronizing transducers.
    F. Olukoya.
    Preprint: arXiv:2004.00516, 1-12.

Published

  1. Automorphisms of the generalized Thompson’s group.
    F. Olukoya.
    Trans. London Math. Soc., 9, (2022), 86-135.
    doi:10.1112/tlm3.12044 and arXiv:1908.03816.
  2. Automorphisms of shift spaces and the Higman–Thompson groups: the one-sided case.
    C. Bleak, P. Cameron, F. Olukoya.
    Discrete Analysis 2021:15, 35pp.
    doi:10.19086/da.28243 and arXiv:2004.08478.
  3. Automorphism tower of groups of homeomorphism of Cantor space.
    F. Olukoya.
    Israel Journal of Mathematics Vol. 244, 883–899 (2021).
    doi:10.1007/s11856-021-2196-z and arXiv:1908.03815.
  4. Conjugate subgroups and overgroups of \(V_n\).
    C. Donoven, and F. Olukoya.
    International Journal of Algebra and Computation Vol. 30, No. 6 (2020) 1129–1160.
    doi:10.1142/S0218196720500344 and arXiv:1710.00913.
  5. The growth rate of automata groups generated by reset automata.
    F. Olukoya.
    To appear, Groups Geometry and Dynamics 1-37.
    arXiv:1709.07209.
  6. The further chameleon groups of Richard Thompson and Graham Higman: automorphisms via dynamics for the Higman groups \(G_{n,r}\).
    To appear, Memoirs of the AMS, 1-96.
    C. Bleak, P. Cameron, Y. Maissel, A. Navas, F. Olukoya.
    arXiv:1605.09302.

Past conference attendances

  • 75th British Mathematical Colloquium, University of Manchester, Manchester, United Kingdom: 17-20 June 2024.

  • University of Glasgow, Glasgow, United Kingom: 13-16 May 2024.

  • GoTh Workshop: Groups of Thompson and their relatives, University of Magdeburg, Magdeburg, Germany: 18-22 September 2023

  • World of Group Craft, online, 26 August 2021.

  • University of New South Wales, Sydney, Australia: 30 March 2021.

  • Symmetry in Newcastle, University of Newcastle, Newcastle, Australia: 2 October 2020.

  • Geometric and Asymptotic Group Theory with Applications (GAGTA) 2020 one day workshop, online: 23 June 2020.

  • University of St Andrews, St Andrews, United Kingdom: 23 June 2020.

  • Groups generalisations and Applications, University of Aberdeen, Aberdeen, United Kingdom: 16 January 2019.

  • École Normale Supérieure, Paris, France, 4-8 December 2017.

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